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Let
h(x) = (g °
f)(x) = \sqrt[]{x+3}

Which of the following could be a possible decomposition of h(x)?

Let h(x) = (g °f)(x) = \sqrt[]{x+3} Which of the following could be a possible decomposition-example-1

2 Answers

6 votes

Answer:

Choice D is correct answer.

Explanation:

We have given composition of two functions.

h(x) = (gof)(x) = √x+3

We have to find the two functions whose composition is given.

The formula to find the composition of functions:

(gof)(x) = g(f(x)

Choose f(x) = x+3

(gof)(x) = g(x+3)

Choose g(x) = √x

(gof)(x) = √x+3

Hence, answer is f(x) = x+3 and g(x) =√x

User Patronics
by
8.7k points
4 votes

Answer:

D.
f(x)= x+3 and
g(x)=√(x)

Explanation:

We are given that,

Composition of two functions f and g is given by,


h(x) = (g\circ f)(x) = √(x+3).

According to the options:

A.
h(x) = (g\circ f)(x) = g(3x)=√(3x)

B.
h(x) = (g\circ f)(x) = g(x)=x+3

C.
h(x) = (g\circ f)(x) = g(√(x))=√(x)+3

D.
h(x) = (g\circ f)(x) = g(x+3)=√(x+3)

Thus, we see that, option D is correct.

Hence,
f(x)= x+3 and
g(x)=√(x) is a possible decomposition of h(x).

User Adnan Aftab
by
8.6k points

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